Digital Signal Processing Reference
In-Depth Information
low
medium
medium
1
1
1
α
1
β
β
1
1
x
1
x
2
y
medium
high
high
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α
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Fig. 11.16
Mamdani FIS as an example of compositional reasoning (min-max)
Fig. 11.17 Defuzzification
by searching of MF
maximum value
Not applicable !
1
1
max
max
0
0
y
y
=?
Defuzzification Methods: Back to Crisp Output Value
Since the FIS scheme output should be crisp (non-fuzzy) to be applied as a control/
protection signal, the fuzzy number obtained after rules' aggregation should be
converted into crisp value. This process is called defuzzification and can be done,
among others, by means of the following methods [
12
]:
• maximum MAX of the fuzzy number (Fig.
11.17
),
• mean value of local maxima MOM (Fig.
11.18
)or
• center of gravity COG/weighted sum approaches (Fig.
11.19
).
The first two abovementioned methods are not always applicable, which is
illustrated in Figs.
11.17
(there is no clear maximum when the MF is partially flat)
and
11.18
(the output value may fall outside of the fuzzy number support). In case
of the COG method the crisp value is defined according to
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